1. Field of the Invention
The present invention relates to a threshold matrix which is compared with a grayscale original image in halftoning the original image, and also relates to a technique for generating the threshold matrix.
2. Description of the Background Art
Conventionally, an AM (Amplitude Modulated) screening where gray levels are represented by changing the size of dots which are regularly arranged, has been used in creating a halftone image for printing from an original image of gray scale (i.e., continuous tone). An FM (Frequency Modulated) screening where gray levels are represented by changing the number of dots of certain size, the dots being irregularly arranged, has been used for the original image in which moire easily arises. The FM screening is specifically used in an inkjet printer in many cases.
In halftoning the original image, a threshold matrix which is compared with the original image is generated and prepared. As a technique for generating the threshold matrix, for example, Japanese Patent Application Laid-Open No. 8-184958 (Document 1) discloses a technique where a plurality of types of basic tiles each of which is an arrangement of two black dots and two white dots in tow rows and two columns are arranged in a threshold matrix area while prohibiting the basic tiles from forming a predetermined prohibited arrangement, to acquire an array of black dots and white dots in a gray level of 50%, and values of 0 and 1 are respectively assigned to the two black dots of each basic tile and values of 2 and 3 are respectively assigned to the two white dots in each basic tile. Then, the threshold matrix area is divided into four divided areas to which values of 0 to 3 are respectively assigned, and a process of further dividing each divided area into four divided areas while assigning values of 0 to 3 to the four divided areas is repeated, to thereby determine a threshold value of each position in the threshold matrix area. In a technique disclosed in Japanese Patent Gazette No. 2622429 (Document 2), an image is generated by applying a blue noise filter to a binary dot profile representing an arrangement of dots in a gray level and a position where a dot should be added in the dot profile is specified on the basis of a gray level of each pixel in a differential image between the image and the original dot profile, to generate a dot profile in the next gray level of the above gray level. This process is repeated to acquire a dot profile in each gray level and thereby, a blue noise mask (threshold matrix) is generated.
Japanese Patent Application Laid-Open No. 7-170400 discloses a technique where all of the OFF pixels are identified as candidate pixels in a matrix which is in an initial state corresponding to the lowest tone level, a cost value for each candidate pixel based on a radial distance and a relative angle between the candidate pixel and each ON pixel is obtained, and a candidate pixel whose cost value is minimum is made ON, to thereby generate a dither matrix (threshold matrix).
In the meantime, to reduce graininess (reduce granularity) is required in the halftone image which is generated by halftoning the original image. In the technique of Document 1, since it is prohibited only black dots or white dots are arranged in an area of two rows and two columns in an arrangement of the basic tiles, it is possible to reduce graininess in a halftone image corresponding to a gray level of 50%, however, there is a possibility that graininess appears in a halftone image corresponding to another gray level (specifically, a gray level away from 50%). In the technique of Document 2, there is a case where granularity occurs in a halftone image, depending on a distribution in a white noise pattern which is given as the initial condition in generation of the dot profile in a gray level of 50% which is the initial dot profile. Further, since a distance between dots is not considered in generation of the dot profile representing an arrangement of dots in each gray level, it is thought that graininess becomes larger in a gray level away from 50%.